Math Problem Statement
resolver por variación de parámetro
Solution
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Math Problem Analysis
Mathematical Concepts
Differential Equations
Second-Order ODE
Non-homogeneous Equations
Formulas
y'' + 9y = sen(3x)
General solution to homogeneous equation: y_h(x) = c_1 cos(3x) + c_2 sin(3x)
Particular solution form using variation of parameters: y_p(x) = u_1(x) cos(3x) + u_2(x) sin(3x)
Wronskian: W(y_1, y_2) = y_1(x) y_2'(x) - y_1'(x) y_2(x)
Theorems
Variation of Parameters
Trigonometric Identities
Wronskian Determinant
Suitable Grade Level
University Level (Undergraduate Mathematics)
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